Abstract
We consider a general matrix iterative method of the type Xk+1=Xkp(AXk) for computing an outer inverse AR(G),N(G)(2), for given matrices A∈Cm×n and G∈Cn×m such that AR(G)⊕N(G)=Cm. Here p(x) is an arbitrary polynomial of degree d. The convergence of the method is proven under certain necessary conditions and the characterization of all methods having order r is given. The obtained results provide a direct generalization of all known iterative methods of the same type. Moreover, we introduce one new method and show a procedure how to improve the convergence order of existing methods. This procedure is demonstrated on one concrete method and the improvement is confirmed by numerical examples.
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